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Karzai offers to inaugurate Afghan parliament next week

NEW: Lawmakers counter Karzai by asking him to dissolve the special court

Karzai tries to end the political standoff with a promise of inauguration

Karzai's office had announced a one-month inauguration delay

The United Nations says it has "deep concern and surprise" over the call for a delay

Kabul, Afghanistan (CNN) -- Afghan President Hamid Karzai offered Saturday to end a political standoff and move up the inauguration of parliament after hours of heated debate among the country's lawmakers, officials said.

Still, the talks -- described by Mirwas Yasin, a member of parliament, as "hectic and not smooth" -- continued amid ongoing disputes over how to handle not only parliament's future but also an investigation into alleged voter fraud.

Karzai initially had postponed the ceremony by a month, but appeared to concede to demands and offered to inaugurate parliament on Wednesday.

However, the inauguration will take place only under the condition that lawmakers accept any decision made by a special court established in December, at Karzai's request, to probe hundreds of allegations brought forward by losing candidates, parliament member Baktash Seyawash said.

Lawmakers countered Karzai by asking him to dissolve the special court and have the nation's Supreme Court investigate the cases. They are now waiting for the president to respond.

International and Afghan officials question the legitimacy of the special court as well as its jurisdiction. The Independent Electoral Commission and the Election Complaint Commission are the two bodies with authority to rule on the results.

The former group, the election commission certified the election results at the end of November after throwing out more than a million ballots from around 3,000 polling stations because of suspected fraud.

Karzai's office on Wednesday announced a one-month inauguration delay, saying that the special court on election fraud needed more time to investigate complaints from the losing candidates. The decision drew criticism from the United Nations' mission in Afghanistan, and concern from analysts fearful that it could spark ethnic divisions and more violence.

"The security situation has obviously deteriorated over the last year, but this conflict between the president and parliament has really heightened tensions to the extreme," said Candace Rondeaux, a senior Afghan analyst for the International Crisis Group.

Daud Sultanzai, a losing candidate in provincial elections in Ghazni, said Karzai bowed to forces outside the country in moving up the inauguration.

"Everyone was putting pressure on Karzai to walk on the face of the people of this country," he said.

The U.N. Assistance Mission in Afghanistan said Friday it had "deep concern and surprise" about the inauguration delay and urged all parties to adhere to the country's constitution.

"Afghanistan's peaceful future lies in the building up of robust democratic institutions based on the rule of law and clear respect for the separation of powers," it said in a statement.